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Main Authors: Goemaere, Cédric, Oliviers, Gaspard, Bogacz, Rafal, Demeester, Thomas
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.20137
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author Goemaere, Cédric
Oliviers, Gaspard
Bogacz, Rafal
Demeester, Thomas
author_facet Goemaere, Cédric
Oliviers, Gaspard
Bogacz, Rafal
Demeester, Thomas
contents Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated, requiring excessive amounts of compute while struggling to scale to deeper architectures. This paper reformulates PC to overcome this hardware-algorithm mismatch. First, we uncover how the canonical state-based formulation of PC (sPC) is, by design, deeply inefficient in digital simulation, inevitably resulting in exponential signal decay that stalls the entire minimization process. Then, to overcome this fundamental limitation, we introduce error-based PC (ePC), a novel reparameterization of PC which does not suffer from signal decay. Though no longer biologically plausible, ePC numerically computes exact PC weights gradients and runs orders of magnitude faster than sPC. Experiments across multiple architectures and datasets demonstrate that ePC matches backpropagation's performance even for deeper models where sPC struggles. Besides practical improvements, our work provides theoretical insight into PC dynamics and establishes a foundation for scaling PC-based learning to deeper architectures on digital hardware and beyond.
format Preprint
id arxiv_https___arxiv_org_abs_2505_20137
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle ePC: Fast and Deep Predictive Coding for Digital Hardware
Goemaere, Cédric
Oliviers, Gaspard
Bogacz, Rafal
Demeester, Thomas
Machine Learning
Artificial Intelligence
Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated, requiring excessive amounts of compute while struggling to scale to deeper architectures. This paper reformulates PC to overcome this hardware-algorithm mismatch. First, we uncover how the canonical state-based formulation of PC (sPC) is, by design, deeply inefficient in digital simulation, inevitably resulting in exponential signal decay that stalls the entire minimization process. Then, to overcome this fundamental limitation, we introduce error-based PC (ePC), a novel reparameterization of PC which does not suffer from signal decay. Though no longer biologically plausible, ePC numerically computes exact PC weights gradients and runs orders of magnitude faster than sPC. Experiments across multiple architectures and datasets demonstrate that ePC matches backpropagation's performance even for deeper models where sPC struggles. Besides practical improvements, our work provides theoretical insight into PC dynamics and establishes a foundation for scaling PC-based learning to deeper architectures on digital hardware and beyond.
title ePC: Fast and Deep Predictive Coding for Digital Hardware
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2505.20137